Tessellating trimmed NURBS surfaces (Q1344353)

The problem addressed by the authors is triangulation of a surface given by rational tensor splines over a single parameter patch but with arbitrary holes and boundary curves. The simplicial approximation is required to stay within an \(\varepsilon\) distance from the surface in space. This requires the estimation of second partials of rational functions. The complicated computations can be simplified by using homogeneous coordinates when only polynomials have to be differentiated and estimated. A complete outline of the algorithm based on this idea is given together with the discussion of relevant practical problems. In the interior of the parametric domain, the vertices are aligned along scanlines to produce a universally applicable algorithm that depends as little as possible on the configuration to be triangulated and to obtain a net that is as regular as possible in the parameter domain.